Table 3

Example of calculations from data in Baker and Lindeman [Reference 9]

hospital

before" group data

after group data

estimate

std error

weight

n1

e1

P1

n2

e2

p2

y

s

w

1

116

.586

.172

103

.223

.184

-.033

.143

44

2

180

.290

.080

180

.440

.090

.067

.196

24

3

373

.131

.110

421

.587

.100

-.022

.048

208

4

1000

.100

.040

1000

.450

.050

.029

.026

313

5

1298

.000

.074

1084

.480

.065

-.019

.022

333

6

1919

.000

.275

2073

.316

.229

-.146

.044

225

7

3195

.010

.030

3733

.290

.031

.004

.015

365

8

4778

.008

.194

4859

.586

.190

-.006

.014

369

9

4685

.187

.149

6170

.551

.125

-.046

.015

352

10

8108

.467

.248

9918

.678

.280

.152

.031

288

11

11159

.328

.209

11869

.499

.209

.000

.031

288

n1 (n2) = number of subjects in "before" ("after") group. el (e2) = fraction of subjects in "before" ("after") group that had epdiural analgesia, p1 (p2) = fraction of subjects in "before" ("after") group that had a Cesarean section, y= estimated effect of epidural analgesia on the probability of Cesarean section = (p2-p1)/(e2-e1), s= standard error of y= square root of (p2 (1-p2))/n2 + p1 (1-p1)/n1) /(e2-e1)², w^* = weight used in random effects meta-analysis. We computed the weights as follows. Let i index studies, so y_i and s_i are the values of y and s for study i. It is convenient to define w₁ = I/ s_i². Following DerSimonian and Laird [Reference 19], to compute v, the variance of the true effect among the k studies, we set v equal to the larger of (Q-(k-1)) / (Σw_i - Σw_i²/Σw_i) and 0, where Q = Σw_i (y_i - m)², m = Σy_i w_i/Σw_i. The random-effects weights are w^*_i= 1/(s_i² + v), and the summary statistic is y^* = Σy_i w^*_i/Σw^*_i, with standard error s^* = square root of 1/Σw^*_i. Following Proschan and Follman [reference 20], the 95% confidence interval is (y^* - t_k- s^*, y^*+ t_k-1 s^*), where t_k-1 is the value of the 97 ½ percentile of a t-distribution with k-1 degrees of freedom. In this example, k = 11, Q = 50.1, v = .0025, m =-.007, s^* = .019 y^* = -.005, t₁₀ = 2.23, y^* = -.005 and the 95% confidence interval is (-.047, .037).

Baker et al. BMC Medical Research Methodology 2001 1:9   doi:10.1186/1471-2288-1-9